## Concatenations x^2 || 3^2 = y^2

Here are the first few solutions to   $x^2 \; || \; 3^2 \; = \; y^2$

$7^2 \; = \; 49 \; = \; 4 \; || \; 9 \; = \; 2^2 \; || \; 3^2$

$57^2 \; = \; 3249$
$18^2 \; = \; 324$                    $57^2 \; = \; 18^2 \; || \; 3^2$

$253^2 \; = \; 64009$
$80^2 \; = \; 6400$

$253^2 \; = \; 80^2 \; || \; 3^2$

$487^2 \; = \; 237169$
$154^2 \; = \; 23716$

$487^2 \; = \; 154^2 \; || \; 3^2$

$2163^2 \; = \; 4678569$
$684^2 \; = \; 467856$

$2163^2 \; = \; 684^2 \; || \; 3^2$

$9607^2 \; = \; 92294449$
$3038^2 \; = \; 9229444$

$9607^2 \; = \; 3038^2 \; || \; 3^2$

$82137^2 \; = \; 6746486769$
$25974^2 \; = \; 674648676$

$82137^2 \; = \; 25974^2 \; || \; 3^2$

$364813^2 \; = \; 133088524969$
$115364^2 \; = \; 13308852496$

$364813^2 \; = \; 115364^2 \; || \; 3^2$

$3119043^2 \; = \; 9728429235849$
$986328^2 \; = \; 972842923584$

$3119043^2 \; = \; 986328^2 \; || \; 3^2$

$13853287^2 \; = \; 191913560704369$
$4380794^2 \; = \; 19191356070436$

$13853287^2 \; = \; 4380794^2 \; || \; 3^2$

$118441497^2 \; = \; 14028388211601009$
$37454490^2 \; = \; 1402838821160100$

$118441497^2 \; = \; 37454490^2 \; || \; 3^2$

$526060093^2 \; = \; 276739221447168649$
$166354808^2 \; = \; 27673922144716864$

$526060093^2 \; = \; 166354808^2 \; || \; 3^2$

$4497657843^2 \; = \; 20228926072699412649$
$1422284292^2 \; = \; 2022892607269941264$

$4497657843^2 \; = \; 1422284292^2 \; || \; 3^2$

$19976430247^2 \; = \; 399057765413256481009$
$6317101910^2 \; = \; 39905776541325648100$

$19976430247^2 \; = \; 6317101910^2 \; || \; 3^2$

$170792556537^2 \; = \; 29170097368444341432369$
$54009348606^2 \; = \; 2917009736844434143236$

$170792556537^2 \; = \; 54009348606^2 \; || \; 3^2$

$758578289293^2 \; = \; 575441020986694398439849$
$239883517772^2 \; = \; 57544102098669439843984$

$758578289293^2 \; = \; 239883517772^2 \; || \; 3^2$

$6485619490563^2 \; = \; 42063260176370667646056969$
$2050932962736^2 \; = \; 4206326017637066764605696$

$6485619490563^2 \; = \; 2050932962736^2 \; || \; 3^2$

$28805998562887^2 \; = \; 829785553205047909293774769$
$9109256573426^2 \; = \; 82978555320504790929377476$

$28805998562887^2 \; = \; 9109256573426^2 \; || \; 3^2$

$246282748084857^2 \; = \; 60655192004229134301272710449$
$77881443235362^2 \; = \; 6065519200422913430127271044$

$246282748084857^2 \; = \; 77881443235362^2 \; || \; 3^2$

$1093869367100413^2 \; = \; 1196550192280658098507224770569$
$345911866272416^2 \; = \; 119655019228065809850722477056$

$1093869367100413^2 \; = \; 345911866272416^2 \; || \; 3^2$

$9352258807734003^2 \; = \; 87464744806838235291767602404009$
$2957443909981020^2 \; = \; 8746474480683823529176760240400$

$9352258807734003^2 \; = \; 2957443909981020^2 \; || \; 3^2$

$41538229951252807^2 \; = \; 1725424547483155772999508825379249$
$13135541661778382^2 \; = \; 172542454748315577299950882537924$

$41538229951252807^2 \; = \; 13135541661778382^2 \; || \; 3^2$